Modelling and simulation of transient noise in circuit simulation

Abstract

Abstract This paper presents a new approach to the transient noise analysis of integrated circuits. This approach consists of two parts, the modelling of noise sources in the time domain and the development of numerical schemes for stochastic differential-algebraic equations. The noise sources include thermal noise, shot noise, and flicker noise and their modelling is based on generalized stochastic processes. Brownian motion is the starting point for the modelling of white-noise sources (thermal and shot noise), while fractional Brownian motion is used for flicker noise sources. The numerical schemes employed for the computation of solution paths adapt well-known methods for stochastic differential equations to the specific situation within circuit simulation. Under the assumption of small noise the convergence properties of the drift-implicit Euler scheme and the drift-implicit Milstein scheme are proved. Finally numerical experiments with real-world circuits are presented.